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https://open.uns.ac.rs/handle/123456789/10363
Title: | A uniformly accurate spline collocation method for a normalized flux | Authors: | Surla K. Uzelac, Zorica |
Issue Date: | 1-Apr-2004 | Journal: | Journal of Computational and Applied Mathematics | Abstract: | We are concerned with a two-point boundary value problem for a semilinear singularly perturbed reaction-diffusion equation with a singular perturbation parameter ε. Our goal is to construct global ε-uniform approximations of the solution y(x) and the normalized flux P(x)=ε(d/dx)y(x), using the collocation with the classical quadratic splines u(x)∈C 1 (I) on a slightly modified piecewise uniform mesh of Shishkin type. The constructed approximate solution and normalized flux converge ε-uniformly with the rate O(n -2 ln 2 n) and O(n -1 ln n), respectively, on the Shishkin-type mesh, and with O(n -1 ln -2 n) and O(ln -3 n) when the mesh has to be modified. We present numerical experiments in support of these results. © 2003 Elsevier B.V. All rights reserved. | URI: | https://open.uns.ac.rs/handle/123456789/10363 | ISSN: | 3770427 | DOI: | 10.1016/j.cam.2003.09.021 |
Appears in Collections: | FTN Publikacije/Publications |
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